Je mange la carotte.

La is the definite article in French, equivalent to the in English. You use it when you’re referring to a specific carrot already known to both speaker and listener.

• Une would be an indefinite article (a/an) and introduce a carrot for the first time, without specifying which one.
  So Je mange la carotte = “I’m eating the carrot (we both know which one).”
  Whereas Je mange une carotte = “I’m eating a carrot (just any carrot, not a particular one).”

De la is a partitive article used with uncountable nouns (e.g. de la soupe, “some soup”). Since carotte is countable, French prefers:

• Une carotte for “one carrot.”
• Des carottes for “some carrots” (an unspecified number).
  It would sound odd to say Je mange de la carotte, because you’d normally imply whole carrots rather than an unmeasured amount of carrot “matter.”

French noun gender is often arbitrary, but there are patterns you can learn:

• Many nouns ending in -ette are feminine (e.g. la baguette, la lunette).
  In practice you’ll have to memorize the gender with each noun or use a dictionary.

No. Unlike Spanish or Italian, French almost always requires subject pronouns in statements:

• Je mange (I eat) is correct.
• Mange la carotte without je would sound like an imperative: “Eat the carrot!”

In IPA: [ʒə mɑ̃ʒ la kaʁɔt]
Breakdown:

• Je [ʒə] (“zhuh”)
• mange [mɑ̃ʒ] (“mahⁿzh,” with a nasal vowel /ɑ̃/)
• la [la] (“lah”)
• carotte [kaʁɔt] (“ka-rot,” with a French r and silent final e”)